Laws of Motion

Step 1: Find the friction force for each blockThe friction force is given by: $F_{\;\text{friction}\;}=\mu_k \times m \times g$For block $A$ (mass $=2\,\text{kg}$ ):$F_{K\,A}=0.3 \times 2 \times 10=6\,\text{N}$For block $B$ (mass $=4\,\text{kg}$ ):$F_{K\,B}=0.3 \times 4 \times 10=12\,\text{N}$Step 2: Find the net force on each blockThe net force is the applied force minus friction:For block $A$ :$F_A=20-6=14\,\text{N}$For block $B$ :$F_B=20-12=8\,\text{N}$Step 3: Find the acceleration of each blockUse $a=\;\frac{F_{n\,e\,t}}{m}$ for each block.For block $A$ :$a_A=\;\frac{14}{2}=7\,\text{m/s}^2$For block $B$ :$a_B=\;\frac{8}{4}=2\,\text{m/s}^2$Step 4: Find the ratio of accelerations $\;\frac{a_A}{a_B}=\;\frac{7}{2}$ So, the ratio is $7: 2$.